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Samsung smartphones won the two top slots in a recent survey of customer satisfaction, narrowly edging out Apple's iPhone.

The study is the first by the American Customer Satisfaction Index (ASCI) to focus on smartphone brands.

Samsung’s Galaxy S III and Galaxy Note II tied for first place with a score of 84 out of 100. Apple’s iPhone 5 and 4S were just behind with 82; and the iPhone 4 with 81. The remainder of the 10 slots were taken by Motorola Mobility’s Droid Razr Maxx HD, 80; Galaxy S II, 78; Droid Razr, 77; BlackBerry’s Curve, 67, and the Bold at 64.

One interesting twist: though U.S. consumers gave the edge to phones from Korea’s Samsung, a Korean study using the same methodology as ACSI found that Korean consumers rated the iPhone 5 higher than the Samsung Galaxy S III.

According to the study’s authors, the difference in customers’ satisfaction between the Galaxy S II and S III, shows that Samsung is on a “strong upward trend.” “If the [Galaxy] S IV performs as well, or even better, in the eyes of customers, Samsung could threaten Apple’s dominance in overall customer satisfaction,” according to a statement by ACSI Director David VanAmburg.

A separate ACSI ranking gauges overall customer satisfaction for each company. The most recent ranking, in May 2013, measured satisfaction with the “complete array” of smartphone and feature phone products from several companies. Apple’s overall score was 81, a drop of two points from 2012; Samsung gained 7 points compared to last year, to reach a 2013 score of 76.

The smartphone survey shows Samsung’s strength with U.S. consumers. Yet it’s also striking that the iPhone 4, announced in June 2010 – a 3-year-old smartphone – and the iPhone 4S, announced in October 2011 – nearly two years ago -- are rated as highly as the 9-month-old iPhone 5 and nearly as highly as the much more recent Samsung phones. The S III was announced in May 2012; the Note II in August 2012, and released in October.

The survey is based on 2,500 respondents, who were questioned via phone or email. ACSI uses a complex methodology, which its webpage only describes in high-level conceptual terms.

Essentially, the customer satisfaction score is based on questions designed to assess how customers evaluate a several variables in three categories. One category measures the customer’s “anticipation” of the quality of a company's product, based on past experience with the product, and other inputs. A second measures the customer’s evaluation of the product’s actual quality, based on how well it meets his or her needs, and on reliability. The third major variable measures the “quality relative to price paid.”

Apple has invested heavily in iPhone quality and its ACSI scores reflect that. At least in the short term, the latest scores show that Samsung has succeeded in creating products that can rival Apple’s in customer approval.